How can I make these inner surfaces smooth?
The only way to get rid of these lines inbetween the cutout is to select the affected faces and set them to smooth shading.
You then can select the edges, press CTRL+E and mark them as sharp.

Add an Edge Split modifier and make sure that the Sharp Edges checkbox is active.

Alternatively you can also select all the faces of the model, set the shading to smooth and then add the Edge Split modifier and control the Split Angle.

This should give you the desired effect.